In addition to the Canada Place parking, there is another and cheaper lot nearby - just east of the pier. It offers a shuttle service to the piers, and is secure - it is designed specifically for cruise passengers.
Hope you plan to do some traveling in BC before or after your cruise!
We sailed on the Westerdam, Alaska Inside Passage, from Vancouver last July.
We used CruisePark (I don't know the phone #) which is right there at the pier and you just drive up to the terminal where they take your car to a secure place. At the end of the cruise, they bring it back to you ! Contact your travel agent for more info. It worked well for us.